The selective hydrogenation of unsaturated hydrocarbons, and especially the hydrogenation of acetylene which is present as an impurity in mono-olefin-containing streams (e.g., ethylene streams from thermal ethane crackers), is commercially carried out with an alumina-supported palladium/silver catalyst, substantially in accordance with the disclosure in U.S. Pat. No. 4,404,124 and its division, U.S. Pat. No. 4,484,015, the disclosures of both patents being incorporated herein by reference. The operating temperature for this process is selected such that essentially all acetylene is hydrogenated to ethylene while only an insignificant amount of ethylene is hydrogenated to ethane. It is desirable to minimize hydrogenation of ethylene to ethane in order to minimize ethylene losses and to avoid a “runaway” reaction which is difficult to control, as has been pointed out in the above-identified patents. The selective acetylene hydrogenation process can be most effectively controlled when there is a large difference between the temperature at which essentially all acetylene is hydrogenated and a higher temperature at which excessive ethylene-to-ethane conversion occurs.